A dual-clutch transmission (DCT) combines certain features of manual and automatic transmissions. In a DCT, a first input clutch is applied along with a particular gear fork and synchronizer to engage an oddly-numbered gear of a gearbox, i.e., 1st gear, 3rd gear, 5th gear, etc. A separate second input clutch is applied with a different gear fork and synchronizer to engage an even gear such as 2nd gear, 4th gear, 6th gear, and the like. A transmission control module predicts a desired gear using various available control inputs, for instance engine acceleration and vehicle braking levels. The transmission control module then commands engagement of the particular gear fork used for the desired gear, with gear fork engagement occurring prior to engagement of the input clutch needed for the desired gear. Due to its unique construction, a DCT may provide faster shift speeds relative to those of a conventional automatic transmission, with improved overall shift control and increased post-shift power.